Question

1. determine the angle and direction of rotation about the origin for the transformation shown to the right.
2. (sbac) let r(3, 1) be a point on a polygon, and r be the corresponding point on a new image. the figure is translated by using (x, y)→(x - 1, y + 4) to arrive at r. what are the coordinates of r?

Explanation:

Step1: Analyze rotation for question 5

Observing the figure, the object rotates 90 - degrees counter - clockwise about the origin.

Step2: Apply translation rule for question 6

Given the translation rule \((x,y)\to(x - 1,y + 4)\) and the point \(R(3,1)\). For the \(x\) - coordinate of \(R'\), we have \(x'=3-1 = 2\). For the \(y\) - coordinate of \(R'\), we have \(y'=1 + 4=5\).

Answer:

1. Angle: 90 degrees, Direction: Counter - clockwise
2. The coordinates of \(R'\) are \((2,5)\)